A Foundational Theory of Information Based on Inference

Project ID: 2531bd1693

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Research Theme: Information and Communication Technologies

Research Area(s): Logic & Combinatorics (especially proof theory)
Theoretical computer science (especially logic, abstract models, logical concepts, semantics)

UCL Lead department: Philosophy

Department Website

Lead Supervisor: Tim Button

Project Summary:

Information is one of the most widely-used concepts of our times. But it has not yet been given convincing logical or mathematical foundations. Without them, we lack adequate reasoning tools for understanding the complex ecosystems of systems, including AI systems, upon which the society depends.

This project will rectify this by developing an inferentialist semantic theory of information. There are three key components:

  1. CONCEPTUAL ANALYSIS. The project begins with a philosophically precise account of the concepts required for an inferentialist account of information (there is at present no such inferentialist account in the literature). Dretske expressed the key concepts of information in terms of intentionality, truth, and transmissibility (in ‘Metaphysics of Information’); we crucially replace truth with inferability, and trace the consequences of this replacement.

  2. LOGIC. Proof-theoretic semantics (P-tS) provides a mathematical-logical realization of inferentialist reasoning. The project will develop a P-tS for the logical theory of information, capturing the conceptual analysis developed in (1) by developing the mathematical-logical theory of an inferentialist primitive unit of information, the ‘inferon’. This proof-theoretic approach will counterpoint the model-theoretic view of information articulated in ‘situation theory’ (as developed by Barwise, Seligman, Devlin, and others).

  3. SYSTEMS. The P-tS tools developed in (2) will provide the basis for a mathematical account of distributed systems modelling — a key tool from computer science for understanding the organization of information processing systems. This will yield a reasoning-based theory of information flow in models of distributed systems.

This PhD project will be supervised jointly by Professor Tim Button (UCL Philosophy) and Professor David Pym (UCL Computer Science and Institute of Philosophy, University of London). Applicants should hold or be about to obtain a strong Master-level degree in philosophy, mathematics, or computer science, and a strong background and interest in logic.